Mach Reflection

MPhil thesis

At school we learnt that with light, the angle of incidence is the same as the angle of refraction. For shocks reflections this isn’t the case. Whilst it is true to say that the angle of incidence is relatively close to the angle of refraction for a weak shock wave. However for certain angles of incidence the point of reflection is away from the hard surface of reflection, there is a strong shock which meets the incidence and reflected shock forming a “triple point” of shocks. The shape of the strong shock has been a hotly contested shape and that was one of the questions I answered.

My work on Mach reflection was split into two difference cases, I examined the actual shape of the stem as a perturbation from the von Neumann criterion for mechanical equilibrium. I wasn’t able to drive a complete equation for the stem but I did manage to derive an equation for the shape of the stem close to the triple point. I conjecture that a full equation may be obtained if the governing equations are solved with an appropriate Green’s function and then examined at the stem boundary. I was nonetheless able to obtain a shape by solving the equations numerically using the Thomas technique.

The other part of my thesis was to examine the shape of the downstream contact discontinuity, this was done in terms of von Mieses variables which are known alternatively as “body-fitted” co-ordinates. These co-ordinates take the streamlines as a co-ordinate. An exact asymptotic expression was derived for this.

The thesis itself contains a complete introduction to shock physics with explicit derivations of all the basic equations used. As the degree was sponsored by AWE, I also did the shock physics for materials whose equation of state (EoS) obeys U_s=a+b*u_p, where and b are constants defining the material.